Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations
CoRR(2024)
摘要
This paper provides rigorous error bounds for physics-informed neural
networks approximating the semilinear wave equation. We provide bounds for the
generalization and training error in terms of the width of the network's layers
and the number of training points for a tanh neural network with two hidden
layers. Our main result is a bound of the total error in the
H^1([0,T];L^2(Ω))-norm in terms of the training error and the number of
training points, which can be made arbitrarily small under some assumptions. We
illustrate our theoretical bounds with numerical experiments.
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